Reassessing delayed and forgone marriage in the United States

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## Reassessing delayed and forgone marriage in the United States

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**1. **Reassessing delayed and forgone marriage in the United States
Steve Martin
Department of Sociology
University of Maryland – College Park
smartin@socy.umd.edu

**3. **Cohort marriage models: a way to predict timing and prevalence of marriage. In a cohort marriage model, the proportion of women marrying at age t is a function of t.
The functional form is the same across cohorts and across nations, but a few key parameters are allowed to vary.
We use the relative frequency distribution of marriages at each year of age up to T to estimate the parameters of the nuptiality model for a given cohort.
Once we have estimated the parameters for a cohort, we can project the proportion of that cohort that will marry at any future year of age.

**4. **Functional forms of two common cohort marriage models: Coale-McNeil Model:
g(a) = (E/?)*1.2813*exp{-1.145*[(a-?)/? + .805]– exp[-1.896*[(a-?)/? + .805]]}
where g(a) is the proportion marrying at age a in the observed population,
? is the mean age at marriage for those ever marrying,
? is the standard deviation of age at marriage for those ever marrying, and
E is the proportion who ever marry.
Hernes Model:
d(Pt)/dt = A * bt * (1- Pt) * (Pt)
where t is a year of age,
and Pt is the proportion of the cohort marrying at age t

**5. **Strengths of cohort nuptiality models: Nuptiality models work very well for historical populations:
“The most puzzling feature of the common pattern of first-marriage frequencies is its very prevalence. We have seen evidence of the same basic curve of first marriages in cohorts that marry early and cohorts that marry late, in cohorts in which marriage is virtually universal, and in cohorts in which one-quarter remain single.” Ansley Coale, 1971.
To some extent, the functional forms of nuptiality models permit a behavioral interpretation
A double exponential function is consistent with a two-stage marriage process: 1.) searching for a partner. 2.) entering a marriage once one has found a suitable marriage partner.

**6. **A crucial sociological distinction: delayed or forgone marriage. Forgone marriage:
net reduction in the total proportion of individuals marrying.
Delayed marriage:
marriages occur at later ages with (little or) no net reduction in the total proportion of individuals marrying.

**7. **The idea of forgone marriage figures prominently in cohort marriage models “It is indeed mystifying that the presence of a large reservoir of women remaining single in Sweden did not produce a pattern of first marriage frequencies essentially different from the pattern in Taiwan. It is as if those designated to remain unmarried had been designated at birth as ineligible, and the experience of the remainder – those fated for marriage – was unaffected by their existence.”
Ansley Coale, 1971
If this is so, it should be possible to predict future marriage behavior based on incomplete observations of marriage cohorts!

**8. **Weaknesses of nuptiality models Working “very well” has never been clearly defined.
It may be that nuptiality models have stopped working “very well” for recent cohorts.
Bloom and Bennett 1990: (Coale-McNeil Model)
predicted a decline in total proportions marrying for women of all races and educational categories
a preliminary version of the paper in 1985 caused a minor panic among college educated women after it appeared in the NY Times.
Goldstein and Kinney 2001: (Hernes Model)
predicted 3% would never marry among white women with a college degree born in 1960-1964 (with 6% still never-married as of 2004)
as of June 2004 CPS: 11.6% remain never-married.

**9. **A low-tech alternative to cohort nuptiality models: projection from age-specific marriage rates
Given a cohort of women that has not yet completed marriage formation (say, by age 45):
1.) For all observed years of age, record the age-specific marriage rates
2.) For unobserved years of age, substitute the age-specific marriage rates from the most recent observed cohort.
see Rindfuss, Morgan, and Swicegood (1988).

**10. **Possible weaknesses of the low-tech approach. 1.) In a time of delayed marriage and rising marriage rates at older ages, projection from previous age-specific marriage rates may under-predict older-age marriage formation.
see Ryder 1990.
2.) Some women in every cohort will never marry (a form of unmeasured heterogeneity)
Even if this proportion does not change as a percent of subsequent cohorts, it will change as a percent of each cohort that is unmarried at age t; hence, overall marriage rates at age t will not be constant across cohorts.
3.) Working “very well” has still not been clearly defined.

**11. **My approach: adjust projections under a range of possible age-specific marriage rates It is difficult to identify individual-specific heterogeneity in the propensity to marry, and impossible in large-sample surveys that are available.
however, it is relatively easy to predict the effects of such heterogeneity across the range of all plausible values.
One also cannot predict period trends in age-specific marriage rates.
however, one can identify linear age*cohort trends across previous cohorts, net of heterogeneity, and predict the effects of continuation of such trends if they were to continue.

**12. **Data 1996 and 2001 Surveys of Income and Program Participation (SIPP) Wave II Topical Modules.
Sample restricted to women born in the U.S. between 1945 and 1974.
N = 31,798

**13. **Sources of uncertainty in the projections Sampling variation: accounted in the estimation procedure.
Response error: probably small.
Nonrandom sampling/complex sample design: not accounted in the estimation procedure - SIPP documentation recommends a standard error multiplier of 1.9.
Model assumptions: accounted in the estimation procedures, across the range of models considered.
Uncertainty about the future. ???

**14. **Descriptive Figure 1: First Marriage Rates by Age and Birth Cohort for U.S. White Nonhispanic Women with No Four-Year College Degree.

**15. **Descriptive Figure 2: First Marriage Rates by Age and Birth Cohort for U.S. White Nonhispanic Women with a Four-Year College Degree.

**16. **Figure 3: First Marriage Rates for U.S. White Nonhispanic Women with a Four-Year College Degree, Fitted to a Hernes Model

**17. **Figure 4 (From Table 2): Projected Proportions of US Born White Nonhispanic Women Never-Married at Age 45.

**18. **Summary More college graduates are remaining unmarried than predicted by the Hernes nuptiality model.
For every group except nonhispanic whites with 4-year college degrees, the proportion remaining unmarried appears to be either holding steady or increasing.
Differences by educational group in the proportions ever marrying appear to be diminishing, but are not yet crossing over.

**19. **Assessment of marriage projection using age-specific marriage rates. The “low-tech” projection technique using age-specific marriage rates (unexpectedly) produces an estimate in the middle of the range across possible modeling assumptions.
Uncertainty about modeling assumptions increases the overall uncertainty of the projections, but is still less than uncertainty due to sampling error and (presumably) nonrandom sampling.

**20. **A possible explanation for problems with cohort nuptiality models in recent cohorts. Both the Hernes and Coale-McNeil Models tend to fit age-specific marriage rates to a positively skewed function.
Throughout most of history, age-specific marriage rates were indeed positively skewed.
In recent cohorts, and particularly for college graduate women, we are starting to see negatively skewed patterns of age-specific marriage rates.